Part 91 operation only requires "The aircraft is continuously in a position from which a descent to a landing on the intended runway can be made at a normal rate of descent using normal maneuvers". The touchdown zone referenced in 91.175c applies to 135 and 121 operations and they will have clarification in their op specs.(Which are also legally binding FAA approved documents.)
The interpretations I gather indicate that the touchdown zone means different things in different contexts. I would need to search a bit more but touchdown zone elevation as given on approach plates is measured at a specific point, which if I recall is at the aiming point.(1000ft)
For the airport operator, touchdown zone markings are required only for runways with precision approaches. It is 3000 feet, but there must be a minimum length blank space in the middle so the TDZ can be less than 3000ft for shorter runways or runways with displaced thresholds. The specifics use these documents.
AC 150/5340-1m section 2.7
And 14CFR 152 incorporates a list of Advisory Circulars by reference(Making those ACs regulatory)
Now these provide some nice bureaucratic circular references to each other. But the key part is that an airport requires a set of approved documents that cover the details of the airport. Those operational documents are binding,(explicitly stated in 14 CFR 139) and it is strongly implied that those operational documents must follow the guidelines of the referenced AC on Standards for Airport Markings.
AH HAA! More applicable to flight operations than airport operations: ([IFR]Procedure design standards) FAA Order 8260.3E appendix B-11
- Touchdown zone. The first 3000 feet of runway beginning at the threshold. For helicopter procedures it is identical to the landing area.
- Touchdown zone elevation. The highest runway centerline elevation in the first 3000 feet of the landing surface (touchdown zone).
- Visual descent point. The VDP is a defined point on the final approach course of a nonprecision straight-in approach procedure from which normal descent from the MDA to the runway touchdown point may be commenced, provided visual reference is established.
- Vertical guidance surface. The VGS is a narrow inclined plane centered on the runway centerline that is evaluated for obstructions between the DA/VDP and LTP[landing threshold point] for all straight-in aligned approach procedures.
- Visual glide slope indicator. The VGSI is an airport lighting aid that provides the pilot with a visual indication of the aircraft position relative to a specified glidepath to a touchdown point on the runway. PAPI and VASI are examples of VGSI systems.
And so the touchdown zone is indeed the first 3000 feet and touchdown point is essentially the aiming point used for calculating the glide slope of an approach and position of a vasi/papi. I find it interesting that the procedure design guidelines use the touchdown point as the assumption even for visual approaches. Considering there are runways of only 3000 feet there is still some ambiguity regarding "touchdown zone" in the context of 91.175c and 121.651, but both also state "made at a normal rate of descent using normal maneuvers" implying that the touchdown zone is dependent on the individual operation.(ie. If you would normally land before 2000ft then you your the TDZ for your operation is from threshold to 2000ft and you must be able to hit that same goal without getting fancy.)
In addition, the flight planning portion of a part 119 operation (which is what this whole mess is about) will follow explicit touchdown assumptions required in the company op specs. (ie Runway meets required landing length when calculated from the normal glide slope and aiming point with normal flare) And op specs are legally binding.
If you were to study most of order 8260.3 you would find the intent of 91.175c.(I'm not really suggesting you read all of it, it is a tech spec document targeted at a specific group inside the FAA.) A missed approach executed either beyond the missed approach point or below the minimum approach altitude(decision height) is not assured of obstacle clearance during the missed approach procedure in IMC. As such there should be minimal chance of executing a go around once committed to that final piece of the approach. This climb during missed approach is the reason many procedures have high minimums, obstacles on the approach side are not usually the issue.
Along with all of that you get into the interpretations of common law and generalized regulation that expect a pilot to use good judgement in all matters. So then the relevant touchdown zone is that which would be considered reasonable by a majority of experienced pilots. Making the 3000ft specification quite irrelevant to flight operations and only really applicable to surveyors and runway painting.